Quasi-single-mode optical fiber with a large effective area

ABSTRACT

A quasi-single-mode optical fiber with a large effective area is disclosed. The quasi-single-mode fiber has a core with a radius greater than 5 μm, and a cladding section configured to support a fundamental mode and a higher-order mode. The fundamental mode has an effective area greater than 170 μm 2  and an attenuation of no greater than 0.17 dB/km at a wavelength of 1530 nm. The higher-order mode has an attenuation of at least 1.0 dB/km at the wavelength of 1530 nm. The quasi-single-mode optical fiber has a bending loss of less than 0.02 dB/turn for a bend diameter of 60 mm for a wavelength of 1625 nm.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of priority under 35 U.S.C. §119 ofU.S. Provisional Application Ser. No. 62/056,784 filed on Sep. 29, 2014,which is related to U.S. Provisional Patent Application Ser. No.62/086383, filed Dec. 2, 2014, and entitled “Optical transmissionsystems and methods using a QSM large-effective-area optical fiber,”which application is incorporated herein by reference.

FIELD

The present disclosure relates to optical fibers, and in particularrelates to a quasi-single-mode optical fiber with a large effectivearea.

The entire disclosure of any publication or patent document mentionedherein is incorporated by reference, including the publication by I.Roudas, et al., “Comparison of analytical models for the nonlinear noisein dispersive coherent optical communications systems,” IEEE PhotonicsConference, paper MG3.4, Bellevue, Wash., September 2013; thepublication by Sui et al., “256 Gb/s PM-16-QAM Quasi-Single-ModeTransmission over 2600 km using Few-Mode Fiber with Multi-PathInterference Compensation,” OFC Conference, San Francisco, Calif., Mar.9-13, 2014, Fiber Non-linearity Mitigation and Compensation (M3C) (ISBN:978-1-55752-993-0); and the publication by S. J. Savory, “Digitalfilters for coherent optical receivers,” Optics Express, Vol. 16, No. 2,Jan. 21, 2008, pp. 804-818.

BACKGROUND

Optical fibers are used for a variety of applications, especially inlong-haul, high-speed optical communications systems. Optical fibershave an optical waveguide structure that acts to confine light to withina central region of the fiber. One of the many benefits of opticalfibers is their ability to carry a large number of optical signals indifferent channels, which provides for high data transmission rates anda large bandwidth.

The increasing demand for bandwidth and higher data transmission rateshas resulted in optical fibers carrying more channels and higher amountsof optical power. At some point, however, the optical power carried bythe optical fiber can give rise to non-linear effects that distort theoptical signals and reduce the transmission capacity of the opticalcommunications system. Consequently, there is a practical limit to howmuch optical power an optical fiber can carry.

Because the optical power is confined by the waveguide structure of theoptical fiber, the intensity determines the severity of non-lineareffects in the optical fiber. The intensity is defined as the amount ofoptical power in the guided light divided by the (cross-sectional) areaover which the guided light is distributed. This area is referred to inthe art as the “effective area” A_(eff) of the optical fiber. Theeffective area A_(eff) is calculated from the electromagnetic fielddistribution of the light traveling within the optical fiber usingtechniques and methods known in the art.

It is well-known that optical fibers with large effective areas A_(eff)are desirable in optical transmission systems because of theirrelatively high power threshold for nonlinear distortion impairments.The larger the effective area A_(eff), the lower the intensity and thusthe less non-linear effects. Because of this feature, an optical fiberwith a large effective area A_(eff) may be operated at higher opticalpowers, thereby increasing the optical signal-to-noise ratio (OSNR).

Unfortunately, the effective area A_(eff) of optical fibers cannotsimply be increased without bound. The conventional wisdom in the art isthat an effective area A_(eff) of about 150 μm² is the limit for a truesingle-mode fiber to maintain sufficient bend robustness, (i.e., reducedloss due to bending). In some cases, an effective area A_(eff) of 150μm² may in fact already be too large for some bending-loss requirements.However, the bending loss of an optical fiber can be reduced byincreasing the mode confinement and hence the cutoff wavelength of theoptical fiber associated with single-mode operation. Increasing theeffective area A_(eff) beyond present-day values would require raisingthe cutoff wavelength to be above the signal wavelength, therebyresulting in few-mode operation, which gives rise to undesirable opticaltransmission impairments such as modal dispersion and multipathinterference (MPI).

Alternatives to increasing the effective area A_(eff) of the opticalfiber to reduce adverse non-linear effects include decreasing theeffective nonlinear index n₂. The nonlinear physics of an optical fiberdepends on the ratio n₂/A_(eff). However, changing n₂ is difficult andthe resulting effect is likely to be very small. Reducing the fiberattenuation is another alternative for better transmission performance.A lower fiber attenuation reduces the need for amplification and thusreduces the noise of the transmission link, which in turn reduces therequired signal power for a given required OSNR. However, reducing theattenuation of the optical fiber impacts the optical fiber transmissionsystem in a different way than by changing the effective area A_(eff),so that these two parameters cannot be exactly traded off.

What is needed therefore is a more robust type of large-effective-areaoptical fiber that reduces adverse non-linear effects while also havingsufficiently small bending loss.

SUMMARY

An aspect of the disclosure is a QSM optical fiber. The QSM fiberincludes a core having a centerline and an outer edge, with a peakrefractive index n₀ on the centerline and a refractive index n₁ at theouter edge. A cladding section surrounds the core and has a first innerannular cladding region immediately adjacent the core. The core andcladding section support a fundamental mode LP₀₁ and a higher-order modeLP₁₁ and define: i) for the fundamental mode LP₀₁: an effective areaA_(eff)>170 μm² and an attenuation of no greater than 0.17 dB/km at 1530nm; ii) for the higher-order mode LP₁₁: an attenuation of at least 1.0dB/km at 1530 nm; and iii) a bending loss of BL<0.02 dB/turn at 1625 nmand for a bend diameter D_(B)=60 mm.

In one example of the QSM fiber described above, the effective areaA_(eff)>200 μm² at 1530 nm.

Another aspect of the disclosure is a QSM optical fiber that has a corehaving a centerline and a radius r₁ greater than 5 μm, with a peakrefractive index n₀ on the centerline and a refractive index n₁ at theradius r₁; a cladding section surrounding the core, wherein the claddingsection includes a first inner annular cladding region immediatelyadjacent the core with a minimum refractive index n₂, a second innerannular cladding region immediately adjacent the first inner annularcladding region and having minimum refractive index n₃, and a ringimmediately adjacent the second inner annular cladding region and havinga refractive index n_(R), wherein n₀>n₁>n₃>n₂ and n_(R)>n₃>n₂; whereinthe core and cladding section support a fundamental mode LP₀₁ and ahigher-order mode LP₁₁ and define: i) for the fundamental mode LP₀₁: aneffective area A_(eff)>150 μm² and an attenuation of no greater than0.17 dB/km at 1530 nm; ii) for the higher-order mode LP₁₁: anattenuation of at least 1.0 dB/km at 1530 nm; and iii) a bending loss ofBL<0.02 dB/turn at 1625 nm and for a bend diameter D_(B)=60 mm.

In one example of the QSM fiber described immediately above, theeffective area A_(eff)>170 μm², while in another example, the effectivearea A_(eff)>200 μm². In another example, n₁>n_(R), while in otherexamples n₁=n_(R) and n₁<n_(R).

Another aspect of the disclosure is an optical transmission system thatincludes the QSM optical fiber as disclosed herein. The opticaltransmission system further includes an optical transmitter configuredto emit light that defines an optical signal that carries information;an optical receiver optically coupled to the optical transmitter by theQSM fiber and configured to receive the light emitted by the opticaltransmitter and transmitted over the QSM optical fiber in thefundamental mode LP₀₁ and the higher-order mode LP₁₁ thereby giving riseto multipath interference (MPI), wherein the optical receiver generatesan analog electrical signal from the received light; ananalog-to-digital converter (ADC) that converts the analog electricalsignal into a corresponding digital electrical signal; and a digitalsignal processor electrically connected to the ADC and configured toreceive and process the digital electrical signal to mitigate the MPIand generate a processed digital signal representative of the opticalsignal from the optical transmitter.

Additional features and advantages are set forth in the DetailedDescription that follows, and in part will be readily apparent to thoseskilled in the art from the description or recognized by practicing theembodiments as described in the written description and claims hereof,as well as the appended drawings. It is to be understood that both theforegoing general description and the following Detailed Description aremerely exemplary, and are intended to provide an overview or frameworkto understand the nature and character of the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings are included to provide a furtherunderstanding, and are incorporated in and constitute a part of thisspecification. The drawings illustrate one or more embodiment(s), andtogether with the Detailed Description serve to explain principles andoperation of the various embodiments. As such, the disclosure willbecome more fully understood from the following Detailed Description,taken in conjunction with the accompanying Figures, in which:

FIG. 1 is a front elevated view of a section of quasi-single-mode (QSM)fiber as disclosed herein;

FIG. 2 is a plot of the refractive index n versus radius r thatillustrates an example refractive index profile for an example of theQSM fiber of FIG. 1;

FIG. 3 is similar to FIG. 2 and illustrates an example refractive indexprofile for the QSM fiber that does not include the ring portion of thecladding section;

FIG. 4 is a close-up, cross-sectional view of the QSM fiber of FIG. 1,illustrating an example where the fiber includes an axial (longitudinal)refractive-index perturbation designed to provide substantialattenuation of the higher-order mode while not substantially attenuatingthe fundamental mode;

FIG. 5 is similar to FIG. 2 and illustrates in a single plot threedifferent refractive index profiles p1, p2 and p3 for example QSMfibers, wherein the inner cladding for the different profiles hasdifferent depths;

FIG. 6 is a plot of the bending loss BL (dB/turn) versus the bendingdiameter D_(B) (mm) for the three refractive index profiles p1, p2 andp3 of FIG. 5;

FIG. 7 is a plot of the ratio of the measured outputted optical powerP_(OUT) to the inputted optical power P_(IN) (P_(OUT)/P_(IN)) versus thewavelength λ (nm) for the three different refractive index profiles p1,p2 and p3 of FIG. 5, wherein the plot is used to calculate the cutoffwavelength λ_(c) from multimode to single-mode operation;

FIGS. 8A and 8B plot of the signal power distribution SP in arbitrarypower units (a.p.u.) as a function of the differential mode delay or DMD(ns) in a two-mode (LP₀₁ and LP₁₁) QSM optical fiber for the case wherethere is negligible mean differential modal attenuation or DMA (FIG. 8A)and for the case where there is a high DMA (FIG. 8B), wherein the solidshows the total power, the dashed line shows the power in thefundamental mode LP₀₁, and the dashed-dotted line shows the power in thehigher-order mode LP₁₁;

FIGS. 9A and 9B are plots of the effective DMD, denoted DMD_(Eff),versus the DMA (dB/km) for an example optical transmission system thatemploys an example of the QSM fiber disclosed herein, wherein for FIG.9A the DMD units are nanoseconds whereas in FIG. 9B the DMD_(Eff) is inunits of the tap (temporal) spacing τ of the signal processor; and

FIG. 10 is a schematic diagram of an optical transmission system thatemploys the QSM fiber as disclosed herein along with MPI compensation torecover the signal that travels in the fundamental LP₀₁ mode of the QSMfiber.

DETAILED DESCRIPTION

Reference is now made in detail to various embodiments of thedisclosure, examples of which are illustrated in the accompanyingdrawings. Whenever possible, the same or like reference numbers andsymbols are used throughout the drawings to refer to the same or likeparts. The drawings are not necessarily to scale, and one skilled in theart will recognize where the drawings have been simplified to illustratethe key aspects of the disclosure.

The claims as set forth below are incorporated into and constitute partof this Detailed Description.

Terminology

The term “relative refractive index,” as used herein in connection withthe multimode fibers and fiber cores discussed below, is defined as:

Δ(r)=[n(r)² −n _(S) ²)]/(2n _(S) ²)

where n(r) is the refractive index at radius r, unless otherwisespecified and n_(S) is the reference index. The relative refractiveindex is defined at the operating wavelength λ_(p). In another aspect,n_(S) is the index of undoped silica (SiO₂). The maximum index of theindex profile is denoted n₀, and in most cases, n₀=n(0).

As used herein, the relative refractive index is represented by Δ andits values are given in units of “%,” unless otherwise specified. In thediscussion below, the reference index n_(REF) is that for pure silica.

The term “dopant” as used herein generally refers to a substance thatchanges the relative refractive index of glass relative to pure(undoped) SiO₂ unless otherwise indicated.

The term “mode” is short for a guided mode or optical mode. A“multimode” optical fiber means an optical fiber designed to support thefundamental guided mode and at least one higher-order guided mode over asubstantial length of the optical fiber, such as 2 meters or longer. A“single-mode” optical fiber is an optical fiber designed to support afundamental guided mode only over a substantial length of the opticalfiber, such as 2 meters or longer. A “few mode” or “few-moded” opticalfiber is an optical fiber designed to support a fundamental guided modeand one or two higher-order modes over a substantial length of theoptical fiber, such as 2 meters or longer. A “quasi-single mode” fiberis distinguished from a “few-mode” fiber in that the former seeks to useonly the fundamental mode to carry information while the latter seeks touse all of the few modes to carry information.

The term “cutoff” is used herein refers to the cutoff wavelength λ_(c)that defines the boundary for single-mode and multimode operation of anoptical fiber, wherein single-mode operation of the fiber occurs forwavelengths λ>λ_(c). The cutoff wavelength λ_(c) as the term is usedherein can be measured by the standard 2 m fiber cutoff test, FOTP-80(EIA-TIA-455-80), to yield the “fiber cutoff wavelength,” also known asthe “2 m fiber cutoff” or “measured cutoff”. The FOTP-80 standard testis performed to either strip out the higher order modes using acontrolled amount of bending, or to normalize the spectral response ofthe fiber to that of a multimode fiber.

For examples of the QSM fiber disclosed herein, the cutoff wavelengthλ_(c)>1600 nm, or more preferably λ_(c)>1700 nm, or more preferablyλ_(c)>1750 nm, or even more preferably λ_(c)>1800 nm.

The number of propagating modes and their characteristics in acylindrically symmetric optical fiber with an arbitrary refractive indexprofile is obtained by solving the scalar wave equation (see for exampleT. A. Lenahan, “Calculation of modes in an optical fiber using a finiteelement method and EISPACK,” Bell Syst. Tech. J., vol. 62, no. 1, p.2663, February 1983). The light traveling in an optical fiber is usuallydescribed (approximately) in terms of combinations of LP (linearpolarization) modes. The LP_(0p) modes with p>0 have two polarizationdegrees of freedom and are two-fold degenerate. The LP_(mp) modes withm>0, p>0 have both two polarization and two spatial degrees of freedom.They are four-fold degenerate. In the discussion herein, polarizationdegeneracies are not counted when designating the number of LP modespropagating in the fiber. For example, an optical fiber in which onlythe LP₀₁ mode propagates is a single-mode fiber, even though the LP₀₁mode has two possible polarizations. A few-mode (or “few moded”) opticalfiber in which the L₀₁ and LP₁₁ modes propagate supports three spatialmodes but nevertheless is referred herein as having two modes for easeof discussion.

As used herein, the “effective area” A_(eff) of an optical fiber is thecross-sectional area of the optical fiber through which light ispropagated and is defined as:

${A_{eff} = {2\; \pi \; \frac{\left( {\int_{0}^{\infty}{E^{2}\ r{r}}} \right)^{2}}{\int_{0}^{\infty}{E^{4}\ r{r}}}}},$

where E is the electric field associated with light propagated in thefiber and r is the radius of the fiber. The effective area A_(eff) isdetermined at a wavelength of 1550 nm, unless otherwise specified.

Macrobend performance of the example QSM fibers disclosed herein wasdetermined according to FOTP-62 (IEC-60793-1-47) by wrapping 2 turnsaround a mandrel having a diameter D_(B)(e.g., D_(B)=60 mm) andmeasuring the increase in attenuation due to the bending using anencircled flux (EF) launch condition.

In the discussion below, any portion of the optical fiber that is notthe core is considered part of the cladding, which can have multiplesections. In some of the Figures (e.g., FIG. 1 and FIG. 4), the claddingis shown has having a limited radial extent (e.g., out to radius r_(g))for ease of illustration even though the cladding in principle extendsbeyond this limit.

The C-band is defined as the wavelength range from 1530 nm to 1565 nm;The L-band is defined as the wavelength range from 1565 nm to 1625 nm;and the C+L wavelength band is defined as the wavelength range from 1530nm to 1625 nm.

The limits on any ranges cited herein are considered to be inclusive andthus to lie within the stated range, unless otherwise specified.

QSM Optical Fiber

FIG. 1 is an elevated view of a section of a QSM fiber 10 as disclosedherein. The QSM fiber 10 has a body 11 configured as described below andincludes a centerline 12 that runs longitudinally down the center of theQSM fiber.

FIG. 2 is a plot of the refractive index n versus radius r of QSM fiber10 as measured from centerline 12, illustrating an example refractiveindex configuration (profile) for the QSM fiber. The QSM fiber 10 has acentral core (“core”) 20 with a cladding section 30 surrounding thecore. In an example, core 20 is made primarily silica and preferablyalkali doped, e.g., potassium doped silica. Core 20 is preferablysubstantially free, and preferably entirely free, of GeO₂. Core 20 mayalso include fluorine as a dopant.

The cladding section 30 includes a number of regions, namely a firstinner annular cladding region or “inner cladding” 32, a second innerannular cladding region or “moat” 34 surrounding the inner cladding, andan annular outer cladding region or “ring”38 surrounding moat 34. Theshape of the core 20 is approximately triangular, but can vary from astep profile to an alpha profile. The core 20 has an outer edge 21 at aradius r_(e), which can be considered the core radius, which in exampleis also equal to radius r₁. In one example, the core radius r_(e) orr₁>5 μm, while in another example, r_(e) or r₁>7 μm.

In an example, neither the core 20 nor the cladding section 30 includesgermanium. The different regions of cladding section 30 may be made offluorine-doped silica. In an example, cladding section 30 is doped withfluorine while core 20 is doped with potassium.

The example refractive index profile of the example QSM fiber 10 of FIG.2 can be described by nine fiber parameters (P): Five refractive indicesn₀, n₁, n₂, n₃ and n_(R), and four radii r₁, r₂, r₃ and r_(R). Therefractive index n₀ is the peak refractive index and occurs at r=0,i.e., on centerline 12 within core 20. The refractive index n₁represents the refractive index at the interface between the core 20 andthe adjacent inner cladding 32, i.e., at the core edge 21, which in anexample is associated with radius r_(e). The refractive index n₂represents the minimum refractive index for inner cladding 32. Therefractive index n₃ represents the minimum refractive index for moat 34.The refractive index n_(R) represents the refractive index of ring 38.

In an example, the radius r₁ represents both the radius of core 20 andthe inner radius of inner cladding 32, while the radius r₂ representsthe outer radius of the inner cladding. The radius r₃ represents theouter radius of moat 34. The radius r_(R) represents the inner radius ofring 38. The radius r_(g) represents the radius where ring 38 ends andthe glass coating 39 of refractive index n_(g) that makes up the rest ofthe QSM fiber 10 begins.

In an example, the nine fiber parameters P are designed for a nominalglass radius r_(g)=62.5 μm. Small adjustments, to especially thecladding parameters (r₃, n₃) and ring parameters (n_(R), r_(R)) may berequired if the fiber glass radius r_(g) is changed, which is optionalfor reducing bending loss. In FIG. 1, the core edge radius r_(e) isslightly smaller than the inner cladding radius r₁ due to shortcomingsin the refractive index measurement. In the plot of FIG. 5 discussedbelow, the transition from core 20 to inner cladding 32 is vertical sothat r_(e)=r₁.

In an example embodiment of QSM fiber 10, n₀>n₁>n₃>n₂. In anotherexample, n₁>n_(R), while another example n₁≦n_(R). Also in an example,n_(R)>n₃>n₂.

FIG. 3 is similar to FIG. 2 and illustrates an example refractive indexprofile for an example QSM fiber 10 wherein the cladding region 30 doesnot include the outer ring 38. For the “no-ring” profile of FIG. 3, theinner radius of inner cladding 32 is denoted r_(i) and has an associatedrefractive index n_(i). The shape of the core 20 is approximatelystep-like in the example, but can vary from a step profile to an alphaprofile. The small bumps bi and b2 in the refractive index profile ofFIG. 3 are features arising from the expected draw stress distributionand are not critical to the design. As noted above, the inner radiusr_(i) of inner cladding 32 can be equal to the radius r₁ of core 20.

The QSM fiber 10 disclosed herein has a relatively large effective areaA_(eff), which in one example is A_(eff)>150 μm², while in anotherexample is A_(eff)>170 μm², while yet in another example is A_(eff)>200μm². The QSM fiber 10 is designed to be operated using only thefundamental mode LP₀₁ just as in single-mode fiber, while the oneadditional higher-order mode LP₁₁ is not used. The one additionalhigher-order mode LP₁₁ can impair the transmission of optical signalstraveling in the QSM fiber unless appropriate MP-compensating digitalsignal processing is applied to the received (transmitted) signal.

In an example, the fundamental mode LP₀₁ has a fundamental-modeeffective index, the higher-order mode LP₁₁ has a higher-order-modeeffective index, and wherein a difference Δn_(eff) between thefundamental-mode effective index and the higher-order-mode effectiveindex is |Δn_(eff)|>0.001 at a wavelength of 1550 nm.

Higher-Order-Mode Impairments

The main two impairments caused by the presence of the higher-order modeLP₁₁ in QSM fiber 10 are multipath interference (MPI) and excess loss(EL). An aspect of the disclosure includes using QSM fiber 10 foroptical signal transmission while electronically mitigating MPI of theoptical signal using digital signal processing techniques that are knownin the art and as described in greater detail. The electronic mitigationof MPI effects enables the deployment of QSM fiber 10 in an opticaltransmission system. To this end, in an example, the aforementionedparameters P of QSM fiber 10 are substantially optimized, while theexcess loss EL, which cannot be compensated, is substantially minimized(e.g., made substantially zero). This avoids having the excess loss ELreduce the benefit of having a relatively large effective area A_(eff)used to overcome detrimental non-linear effects, as explained above.

Because the higher-order mode LP₁₁ of QSM fiber 10 is undesirable andunused, the design and configuration of QSM fiber 10 is different thanthat for conventional few-mode optical fibers that seek to transmitinformation in the higher-order modes. In particular, becauseconventional few-mode optical fibers seek to utilize the informationtransmitted in the few higher-order modes, these modes need to haverelatively low differential modal attenuation (DMA). As is explained ingreater detail below, the QSM fiber 10 disclosed herein has relativelyhigh DMA, i.e., the higher-order mode LP₁₁ is intentionally subjected toa relatively large attenuation to reduce the degree of opticaltransmission impairment caused by this higher-order mode.

Ideally, QSM fiber 10 would have a relatively large phase indexdifference between all supported modes to minimize mode-coupling, whileat the same time having a small group index difference between allsupported modes. This latter attribute minimizes the digital signalprocessing required to remove MPI artifacts from the received signal.Unfortunately, this is not possible in fibers with large effective areaA_(eff). Qualitatively, this is because, for any mode, the group index(n_(g)) is related to phase index (or “effective index” n_(e)) asfollows:

$n_{g} = {n_{e} - {\lambda \frac{n_{e}}{\lambda}}}$

The difference in the group index n_(g) between two modes is thereforegiven by:

${\Delta \; n_{g}} = {{\Delta \; n_{e}} - {\lambda \; \Delta \frac{n_{e}}{\lambda}}}$

In the limit of very large effective area A_(eff), the wavelengthdispersion of all modes approaches that of the bulk glass, in which casethe last term in the equation for Δn_(g) vanishes so that Δn_(g)≈Δn_(e).Consequently, one cannot simultaneously have a low mode coupling (largeΔn_(e)) and a small differential mode delay (DMD, small Δn_(g)).

In the QSM fiber 10 disclosed herein, low mode coupling is substantiallypreserved while, as noted above, the DMD is managed by intentionallydesigning the QSM fiber to have as much loss (i.e., a high DMA) aspossible for the higher-order mode LP₁₁. A high DMA reduces the numberof equalizer taps (i.e., memory) required in the digital signalprocessor used for MPI compensation, thereby reducing system complexity,as described below. High DMA values also reduce the total MPI level,which may have an upper limit in terms of the efficacy of the MPIcompensation digital signal processing.

In one example, the DMA for a wavelength of 1530 nm is DMA≧1.0 dB/km,while in another example, the DMA≧4.0 dB/km. Also in one example, thecoupling coefficient CC between the fundamental mode LP₀₁ and thehigher-order mode LP₁₁ at a wavelength of 1530 nm is CC<0.002 km⁻¹,while in another example, the coupling coefficient CC<0.001 km⁻¹.

One way to increase the DMA for the higher-order mode LP₁₁ is to shiftthe cutoff wavelength λ_(c) to its lowest possible value consistent withmacrobend requirements. Another way is to make the higher-order modeslossy in a mode-selective way. FIG. 4 is a close-up cross-sectional viewof a portion of an example QSM fiber 10 that includes an axial(longitudinal) refractive-index perturbation 52. FIG. 4 includes a plotof refractive index n versus the axial distance z down the QSM fiberthat illustrates an example form of the refractive-index perturbationhaving a constant period Λ. The refractive-index perturbation 52 isconfigured to increase the attenuation (DMA) of the higher-order modeLP₁₁ while not substantially increasing the attenuation of thefundamental mode LP₀₁. In an example, refractive-index perturbation 52is in the form of a long-period grating that substantially matches adifference in the effective indices of the higher-order mode LP₁₁ and aradiative cladding mode at the operating wavelength, i.e., a periodΛ≈1/Δn, where Δn is the effective index difference between thehigher-order mode LP₁₁ and the radiative cladding mode).

In an example, axial refractive-index perturbation 52 has a wavelengthresonance and includes a non-constant (e.g., chirped) period Λ thatserves to to widen the bandwidth of the resonance as compared to theconstant period configuration. In an example, axial refractive-indexperturbation 52 can be formed in QSM fiber 10 using known methods, suchas laser irradiation. In an example, the axial refractive-indexperturbation 52 can be formed as the fiber is being drawn, such as byirradiating the fiber with one or more lasers. In an example, the periodΛ of the refractive-index perturbation is chosen such that there issubstantially no resonant coupling of the LP₀₁ and LP₁₁ modes in the C+Lbands, and in an example at a wavelength of 1530 nm.

The so-called “Gaussian Noise (GN)” model of optical transmission positsthat the launch-power-optimized system Q-factor scales with theeffective area A_(eff) as:

Q² ∝ A_(eff) ^(2/3)

so that increasing the effective area A_(eff) from 150 to 175 μm²increases Q² by about 11% or 0.45 dB. Increasing the effective areaA_(eff) from 150 to 250 μm² increases Q² by 41% or 1.5 dB. An examplesimulation was carried out for an erbium-doped fiber-amplified (EDFA)polarization-multiplexed (PM)-16QAM (Quadrature Amplitude Modulation)optical transmission system having 80 channels, a 32 GHz (Nyquist)channel spacing, a 50 km span length, ideal (noise and distortion-free)transmitter and receivers and a QSM fiber 10 with span loss of 0.158dB/km. The simulation shows that increasing the effective area A_(eff)from 150 μm² to250 μm² increases the reach at 11.25 dB from 3000 km to4000 km. Hence, while a 1.5 dB increase in optimal Q² seems small, itcan lead to a significant reach improvement.

This simulation suggests that with 50 km spans, increasing the effectivearea A_(eff) from 150 μm² to250 μm² and increasing the span loss from0.158 dB/km to 0.215 dB/km produces no net change in Q². Hence theexcess loss EL (i.e., the additional loss resulting from mode couplingabove the intrinsic LP₀₁ attenuation) of just 0.057 dB/km can completelyerase the advantage of the increase in effective area A_(eff). An excessloss EL of even 0.01 dB/km can decrease the reach of QSM fiber 10 withan effective area A_(eff)=250 μm² by about 200 km. The advantage oflarge effective area fibers with an effective area A_(eff) of less than250 μm² would likewise be reduced.

It was found through modeling that conventional refractive indexprofiles cannot achieve sufficiently large DMA and effective areasA_(eff) exceeding 175 μm² without also introducing excess macrobendloss. However, it was also found that the judicious addition of the ring38 of increased refractive index n_(R) relative to the refractive indexn_(c) of the outer cladding 34 can enhance the LP₁₁ mode coupling to theglass coating 39, thereby increasing the DMA without significantlyimpacting bend performance. In this regard, the index n_(R) of the ring38 must not exceed the effective index n_(eff) of the fundamental mode.In an example, ring 38 includes at least one absorbing dopant thatcontribute to the attenuation of the higher-order mode LP₁₁. Examples ofabsorbing dopants include titanium or other transition metals. Inanother example, ring 38 does not include any absorbing dopants. In anexample, ring 38 includes fluorine dopant, which is not an absorbingdopant.

Example QSM Fibers

Table 1 below sets forth example QSM fiber parameters P for threeexamples of QSM fiber 10. In the Tables below, P stands for the givenparameter, “MIN1” and “MAX1” stand for first example minimum and maximumvalues for the given parameter, “MIN2” and “MAX2” for second exampleminimum and maximum values for the given parameter, and “MIN3” and“MAX3” for third example minimum and maximum values for the givenparameter. The parameters P in the following Tables are based on QSMfiber 10 having a nominal radius r_(g)=62.5 μm.

TABLE 1 EXAMPLE 1 P MIN0 MAX0 MIN1 MAX1 MIN2 MAX2 n₀ 1.4430 1.44501.4436 1.4448 1.4438 1.4447 n₁ 1.4430 1.4450 1.4430 1.4436 1.4432 1.4434n₂ 1.4400 1.4430 1.4406 1.4419 1.4408 1.4415 n₃ 1.4390 1.4430 1.44061.4422 1.4408 1.4412 r₁ [μm] 5 15 7 12 8 11 r₂ [μm] 25 38 28 35 31 33 r₃[μm] 40 62.5 45 55 48 52 r_(R) [μm] 40 62.5 47 57 50 54

Table 2 below is an alternative representation of the refractive indexdata of Table 1. In Table 2, the refractive index change relative topure silica is used. This refractive index change is represented by therelative refractive index Δ, which is given by

${\Delta = \frac{n^{2} - n_{s}^{2}}{2\; n_{s}^{2}}},$

where n is the refractive index value from the tables above (at 1550 nm)and n_(S)=1.444374, the refractive index of pure silica.

TABLE 2 EXAMPLE 1 USING Δ VALUES P MIN MAX MIN1 MAX1 MIN2 MAX2 Δ₀−9.5082E−04   4.3350E−04 −5.3573E−04   2.9498E−04 −3.9733E−04  2.2573E−04 Δ₁ −9.5082E−04   4.3350E−04 −9.5082E−04 −5.3573E−04−8.1248E−04 −6.7411E−04 Δ₂ −3.0237E−03 −9.5082E−04 −2.6095E−03−1.7114E−03 −2.4714E−03 −1.9878E−03 Δ₃ −3.7137E−03 −9.5082E−04−2.6095E−03 −1.5040E−03 −2.4714E−03 −2.1951E−03 r₁ [μm] 5 15 7 12 8 11R₂ [μm] 25 38 28 35 31 33 r₃ [μm] 40 62.5 45 55 48 52 r_(R) [μm] 40 62.547 57 50 54

The second example of QSM fiber 10 is set forth in Table 3 below andrepresents an example of the “no ring” configuration such as shown inFIG. 3.

TABLE 3 EXAMPLE (NO RING) P MIN MAX MIN1 MAX1 MIN2 MAX2 n₀ 1.4435 1.44451.4437 1.4443 1.4438 1.4442 n₁ 1.4430 1.4450 1.4427 1.4438 1.4430 1.4435n_(i) 1.4410 1.4420 1.4412 1.4418 1.4413 1.4417 n₂ 1.4397 1.4413 1.44001.4412 1.4402 1.4409 n₃ 1.4380 1.4410 1.4387 1.4405 1.4390 1.4402 r₁[μm]5 12 5 10 6 9 r_(i) [μm] 6 13 7 12 7 11 r₂ [μm] 18 33 19 29 20 25

The third example of QSM fiber 10 is set forth in Table 4 below andrepresents another example of the “no ring” configuration.

TABLE 4 EXAMPLE 3 (NO RING) P MIN MAX MIN1 MAX1 MIN2 MAX2 n₀ 1.44351.4445 1.4437 1.4443 1.4438 1.4442 n₁ 1.4425 1.4435 1.4426 1.4433 1.44271.4432 n_(i) 1.4410 1.4420 1.4412 1.4418 1.4405 1.4409 n₂ 1.4397 1.44131.4400 1.4412 1.4402 1.4409 n₃ 1.4380 1.4410 1.4387 1.4405 1.4390 1.4402r₁[μm] 6 14 6 12 7 10 r_(i) [μm] 7 15 8 14 9 13 r₂ [μm] 25 35 20 34 2530

QSM Properties of Example Profiles

FIG. 5 is similar to FIG. 2 and shows first, second and third examplerefractive index profiles p1, p2 and p3 (solid, dashed and dotted lines,respectively) for example QSM fibers 10, wherein the different indexprofiles have different depths for inner cladding 32. FIG. 6 is a plotof the predicted bend loss BL (dB/turn) versus bend diameter D_(B) (mm)at a wavelength of 1625 nm as obtained using optical modeling. The threesolid straight lines in FIG. 5 are approximate upper bounds for theexample profiles p1, p2 and p3 based on fitting the oscillation peaks.All three example profiles p1, p2 and p3 yield a bending loss BL<5mdB/turn at a bend diameter D_(B) of 60 mm.

FIG. 7 is a plot of the ratio of the measured outputted optical powerP_(OUT) to the inputted optical power P_(IN) (P_(OUT)/P_(IN)) versus thewavelength λ (nm) for the three different refractive index profiles p1,p2 and p3 of FIG. 5, wherein the plot is used to calculate the cutoffwavelength λ_(c) from multimode to single-mode operation.

Table 5 below summarizes the predicted optical properties of the threeexample profiles p1, p2 and p3 of FIG. 5. The values for the bendingloss BL are obtained from the straight-line fits of FIG. 6 while thecut-off wavelengths λ_(c) are estimated from the power trace plots ofFIG. 7. The effective area A_(eff) is measured in μm² at λ=1550 nm. Thestraight fiber LP₁₁ mode cutoff wavelength λ_(c) is measured innanometers (nm). The straight-fiber LP₁₁ mode radiative loss at 1550 nmis denoted RL and is measured in dB/km. The fundamental mode macro-bendloss BL is measured in dB/turn at λ=1625 nm and a bend diameter D_(B)=60mm.

TABLE 5 PREDICTED OPTICAL PROPERTIES FOR 3 EXAMPLE PROFILES ProfileA_(eff) [μm²] λ_(c) [nm] RL [dB/km] BL [dB/turn] p1 237 1800 11.4 1.9 ×10⁻³ p2 232 1850 5.1 0.9 × 10⁻³ p3 227 1885 2.3 0.6 × 10⁻³

Relationship Between DMA and N_(T)

One of the advantages of QSM fiber 10 is that it reduces the number oftaps needed for the digital signal processor used for MPI compensationin an optical transmission system. FIGS. 8A and 8B plot the signal powerdistribution SP in arbitrary power units (a.p.u.) as a function of theDMD (ns) in a two-mode (LP₀₁ and LP₁₁) QSM fiber 10. The solid shows thetotal power; the dashed line shows the power in the fundamental modeLP₀₁; the dashed-dotted line shows the power in the higher-order modeLP₁₁.

In FIG. 8A, there is negligible mean DMA, while in FIG. 8B here is ahigh mean DMA. All other fiber parameters P were kept the same, and inboth cases the signal was launched into the fundamental mode LP₀₁ only.The amount of significantly delayed contributions (the tail of thedashed black line) is decreased as the DMA increases. This enables useof a QSM fiber 10 having a relatively large DMD with a digital signalprocessor having a reduced number N_(T) of taps as compared toconventional MPI compensation.

The amount of significantly delayed contributions (the tail of thedashed black line) is decreased as the DMA increases. This enables useof a QSM fiber 10 having a relatively large DMD with a digital signalprocessor having a reduced number N_(T) of taps as compared toconventional MPI compensation.

FIGS. 9A and 9B plot the effective DMD, denoted DMD_(Eff), versus theDMA (dB/km) for an example optical transmission system that utilizes theQSM fiber 10 disclosed herein. In FIG. 9A, the DMD_(Eff) has units ofnanoseconds (ns) while in FIG. 9B the DMD_(Eff) is in units of the tap(temporal) spacing τ of the signal processor, wherein each tap hasduration of 31.25 ps. The effective DMD is defined as the time intervalthat includes 99.95% of the interfering pulse energy and represents theamount of delay the digital signal processor needs to compensate forMPI. The calculations used to generate FIGS. 9A and 9B assume a DMD of 1ns/km and a length L=100 km of QSM fiber 10.

The plots of FIGS. 9A and 9B show the effect of the non-zero DMA on thenumber N_(T) of taps needed to compensate for the optical transmissionimpairment of the information-carrying optical signal traveling in thefundamental mode. The calculation of the required number N_(T) ofequalizer taps is approximate. The calculation is based on a mean MPIcompensation, so the results can be considered as establishing a lowerbound on the number N_(T) of taps.

Optical Transmission System with QSM Fiber

FIG. 10 is a schematic diagram of an example optical transmission system(“system”) 100 that employs the QSM fiber 10 as disclosed herein. System100 includes an optical transmitter 110, a section of QSM fiber 10, anoptical receiver 130, an analog-to-digital converter ADC electricallyconnected to the optical receiver and a digital signal processor DSPelectrically connected to the analog-to-digital converter. Alsooptionally included in system 100 is a decision circuit 150 electricallyconnected to the digital signal processor DSP.

The digital signal processor DSP includes an MPI mitigation system 134that in example includes a plurality of equalizer taps 136. System 10and in particular MPI mitigation system 134 is configured to performelectronic equalization of optical transmission impairments to theoptical signal using methods known in the art. In one example, MPImitigation system 134 includes four finite impulse response (FIR)filters in a butterfly structure (not shown), wherein each filter has anumber of taps 136, which are recursively adjusted based on aleast-mean-square (LMS) algorithm.

The QSM fiber section 10 includes an input end 112 optically connectedto optical transmitter 110 and an output end 114 optically connected tooptical receiver 130, thereby establishing an optical connection betweenthe optical transmitter and the optical receiver. In an example, QSMfiber 10 includes an amplifier 160, e.g., an EDFA.

In the operation of system 100, transmitter 110 generates light 200 thatdefines an input analog optical signal OS that carries information onlyin the fundamental mode LP₀₁. Light 200 enters the input end 112 of QSMfiber 10 and travels the length of the fiber to output end 114. Most oflight 200 travels in the fundamental mode (LP₀₁) while a portion of thelight travels in the higher-order mode LP₁₁. The light 200 is denoted as200′ at the output end of QSM fiber 10 due the light having impairmentsdescribed above by virtue of having traveled through QSM fiber 10.

Optical receiver 130 receives light 200′ as emitted from the output end114 of QSM fiber 10 and converts this light into a corresponding analogelectrical signal SA. The analog electrical signal SA passes throughanalog-to-digital converter ADC, which forms therefrom a correspondingdigital electrical signal SD. The digital electrical signal SD is thenreceived by digital signal processor DSP, which performs digitalprocessing of the digital electrical signal. In particular, the digitalsignal processor DSP is configured to perform equalization of MPI usingMPI mitigation system 134 and the equalizer taps 136 therein based ontechniques known in the art. The digital signal processor DSP outputs aprocessed digital electrical signal SDP that is representative (towithin the limits of MPI mitigation system 134) of the initial opticalsignal OS generated by transmitter 110. The processed digital electricalsignal SDP, which includes the information originally encoded intooptical system OS, continues downstream to be processed as needed (e.g.,by a decision circuit 150) for the given application.

As noted above, the relatively high DMA of ≧1 dB/km or >4 dB/km resultsin less complex digital signal processing, i.e., the number N_(T) ofequalizer taps 136 is reduced as compared to conventional opticaltransmission systems that employ MPI compensation. Also, as noted above,high DMA values also reduce the total MPI level, which may have an upperlimit in terms of the efficacy of the MPI compensation digital signalprocessing.

It will be apparent to those skilled in the art that variousmodifications to the preferred embodiments of the disclosure asdescribed herein can be made without departing from the spirit or scopeof the disclosure as defined in the appended claims. Thus, thedisclosure covers the modifications and variations provided they comewithin the scope of the appended claims and the equivalents thereto.

What is claimed is:
 1. A quasi-single-mode (QSM) optical fiber,comprising: a core having a centerline and an outer edge, with a peakrefractive index n₀ on the centerline and a refractive index n₁ at theouter edge; a cladding section surrounding the core, wherein thecladding section includes an inner annular moat region immediatelyadjacent the core; wherein the core and cladding section support afundamental mode LP₀₁ and a higher-order mode LP₁₁ and define: i) forthe fundamental mode LP₀₁: an effective area A_(eff)>170 μm² and anattenuation of no greater than 0.17 dB/km of at 1530 nm; ii) for thehigher-order mode LP₁₁: an attenuation of at least 1.0 dB/km at 1530 nm;and iii) a bending loss of BL<0.02 dB/turn at 1625 nm and for a benddiameter D_(B)=60 mm.
 2. The QSM optical fiber according to claim 1,wherein the core has a radius that is greater than 5 μm.
 3. The QSMoptical fiber according to claim 2, wherein the core radius is greaterthan 7 μm.
 4. The QSM optical fiber according to claim 2, furthercomprising a 2m cutoff wavelength λc>1600 nm.
 5. The QSM optical fiberaccording to claim 4, wherein the first inner annular cladding regionhas a minimum refractive index n₂, and wherein the cladding sectionfurther includes a moat immediately adjacent the inner annular claddingregion and having minimum refractive index n₃.
 6. The QSM optical fiberaccording to claim 5, wherein the cladding section further includes aring immediately adjacent the moat, the ring having a refractive indexn_(R), and wherein n_(R)>n₃>n₂.
 7. The QSM optical fiber according toclaim 6, wherein the ring includes an absorbing dopant that contributeto the attenuation of the higher-order mode.
 8. The QSM optical fiberaccording to claim 1, wherein the effective area A_(eff)>200 μm².
 9. TheQSM optical fiber according to claim 1, wherein: i) the core is made ofpotassium-doped silica; ii) the cladding section is made offluorine-doped silica; and iii) neither the core nor the claddingsection includes germanium.
 10. The QSM optical fiber according to claim1, wherein the attenuation of the fundamental mode LP₀₁ is no greaterthan 0.165 dB/km, and wherein for the fundamental mode LP₀₁ the bendingloss BL<0.005 dB/turn at 1625 nm for the bend diameter D_(B)=60 mm. 11.The QSM fiber according to claim 1, further comprising an axial periodicrefractive-index perturbation configured to contribute to theattenuation of the higher-order mode LP₁₁ while not substantiallyattenuating the fundamental mode LP₀₁.
 12. An optical transmissionsystem, comprising: the QSM optical fiber of claim 1; an opticaltransmitter configured to emit light that defines an optical signal thatcarries information; an optical receiver optically coupled to theoptical transmitter by the QSM fiber and configured to receive the lightemitted by the optical transmitter and transmitted over the QSM opticalfiber in the fundamental mode LP₀₁ and the higher-order mode LP₁₁thereby giving rise to multipath interference (MPI), wherein the opticalreceiver generates an analog electrical signal from the received light;an analog-to-digital converter (ADC) that converts the analog electricalsignal into a corresponding digital electrical signal; and a digitalsignal processor electrically connected to the ADC and configured toreceive and process the digital electrical signal to mitigate the MPIand generate a processed digital signal representative of the opticalsignal from the optical transmitter.
 13. A quasi-single-mode (QSM)optical fiber, comprising: a core having a centerline and a radius r₁greater than 5 μm, with a peak refractive index n₀ on the centerline anda refractive index n₁ at the radius r₁; a cladding section surroundingthe core, wherein the cladding section includes a first inner annularcladding region immediately adjacent the core with a minimum refractiveindex n₂, a second inner annular cladding region immediately adjacentthe first inner annular cladding region and having minimum refractiveindex n₃, and a ring immediately adjacent the second inner annularcladding region and having a refractive index n_(R), wherein n₀>n₁>n₃>n₂and n_(R)>n₃>n₂; wherein the core and cladding section support afundamental mode LP₀₁ and a higher-order mode LP₁₁ and define: i) forthe fundamental mode LP₀₁: an effective area A_(eff)>150 μm² and anattenuation of no greater than 0.17 dB/km at a wavelength of 1530 nm;ii) for the higher-order mode LP₁₁: an attenuation of at least 1.0 dB/kmfor the wavelength of 1530 nm; and iii) a bending loss of BL<0.02dB/turn when the wavelength is 1625 nm and for a bend diameter D_(B)=60mm.
 14. The QSM optical fiber according to claim 13, wherein the coreradius is greater than 7 μm.
 15. The QSM optical fiber according toclaim 13, further comprising a 2m cutoff wavelength λc>1600 nm.
 16. TheQSM optical fiber according to claim 13, wherein the effective areaA_(eff)>170 μm².
 17. The QSM optical fiber according to claim 13,wherein the attenuation of the fundamental mode LP₀₁ is no greater than0.165 dB/km, and wherein for the fundamental


18. The QSM fiber according to claim 13, further comprising an axialperiodic refractive-index perturbation configured to contribute to theattenuation of the higher-order mode LP₁₁ while not substantiallyattenuating the fundamental mode LP₀₁.
 19. The QSM fiber according toclaim 13, further comprising an LP⁰¹-to-LP₁₁ coupling coefficientCC<0.002 km⁻¹ at the wavelength of 1530 nm.
 20. An optical transmissionsystem, comprising: the QSM optical fiber of claim 13; an opticaltransmitter configured to emit light that defines an optical signal thatcarries information; an optical receiver optically coupled to theoptical transmitter by the QSM fiber and configured to receive the lightemitted by the optical transmitter and transmitted over the QSM opticalfiber in the fundamental mode LP₀₁ and the higher-order mode LP₁₁thereby giving rise to multipath interference (MPI), wherein the opticalreceiver generates an analog electrical signal from the received light;an analog-to-digital converter (ADC) that converts the analog electricalsignal into a corresponding digital electrical signal; and a digitalsignal processor electrically connected to the ADC and configured toreceive and process the digital electrical signal to mitigate the MPIand generate a processed digital signal representative of the opticalsignal from the optical transmitter.